Express your answer as a mixed number simplified to lowest terms. $18\dfrac{1}{4}-3\dfrac{6}{12} = {?}$
Solution: Simplify each fraction. $= {18\dfrac{1}{4}} - {3\dfrac{1}{2}}$ Find a common denominator for the fractions: $= {18\dfrac{1}{4}}-{3\dfrac{2}{4}}$ Convert ${18\dfrac{1}{4}}$ to ${17 + \dfrac{4}{4} + \dfrac{1}{4}}$ So the problem becomes: ${17\dfrac{5}{4}}-{3\dfrac{2}{4}}$ Separate the whole numbers from the fractional parts: $= {17} + {\dfrac{5}{4}} - {3} - {\dfrac{2}{4}}$ Bring the whole numbers together and the fractions together: $= {17} - {3} + {\dfrac{5}{4}} - {\dfrac{2}{4}}$ Subtract the whole numbers: $=14 + {\dfrac{5}{4}} - {\dfrac{2}{4}}$ Subtract the fractions: $= 14+\dfrac{3}{4}$ Combine the whole and fractional parts into a mixed number: $= 14\dfrac{3}{4}$